Brownian motion, obstacles and random media:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
[1998]
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 353 S. graph. Darst. |
| ISBN: | 3540645543 9783540645542 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Preface V
Table of Contents VII
Introduction IX
Part I. SOME TOOLS
1. The Feynman Kac Formula and Semigroups 3
1.1 Feynman Kac Formula in a Classical Context 3
1.2 The Class Kd 7
1.3 Semigroups, Kernels of Semigroups 13
1.4 Quadratic Forms, Dirichlet Forms 20
1.5 Notes and References 37
2. Some Potential Theory 39
2.1 A Warm up Calculation 39
2.2 Some Facts about Green Functions 43
2.3 Last Visit and Equilibrium Problem 51
2.4 Maximum Principle, Exceptional Sets, Variational Principle.. 67
2.5 Some Connections with Dirichlet Forms 85
2.6 Notes and References 88
3. Some Principal Eigenvalue Estimates 91
3.1 General Results 91
3.2 Capacity and Principal Eigenvalues 107
A. An Inequality of Thirring and Variation 107
B. The Constant Capacity Regime 116
3.3 Some One dimensional Estimates 121
3.4 Notes and References 135
Appendix: Brownian Bridge Measures 137
VIII Table of Contents
Part II. BROWNIAN MOTION AND RANDOM OBSTACLES
4. The Method of Enlargement of Obstacles 143
4.1 Orientation 143
4.2 Eigenvalue Estimates 150
4.3 Capacity and Volume Estimates 167
4.4 Principal Eigenvalues and Poissonian Obstacles 182
A. Geometric Controls 182
B. Confidence Intervals 185
C. Almost sure Behavior 191
4.5 Large time Wiener Asymptotics 194
A. Quenched Asymptotics 196
B. Annealed Asymptotics 200
4.6 Notes and References 214
5. Lyapunov Exponents 217
5.1 Orientation 217
5.2 Quenched Lyapunov Exponents 221
5.3 Annealed Lyapunov Exponents 239
5.4 Some Large Deviation Estimates 248
5.5 Notes and References 262
6. Quenched Path Measure and Pinning Effect 265
6.1 Heuristics 265
6.2 Prom Weak to Strong Pinning 272
6.3 Random Scales 281
6.4 Coarse Graining of Path Space 286
A. The Forest and Clearings Picture 287
B. Excursion Systems and Coarse Graining 290
6.5 Applications 300
A. Finer Asymptotics for St,u 300
B. Pinning Effect 302
6.6 Notes and References 312
7. Overview, further Results and Problems 313
7.1 Normalizing Constants and Diagonal Behavior 313
7.2 Off diagonal Behavior 322
7.3 Asymptotic Behavior under Weighted Path Measures 335
References 343
Index 351
|
| any_adam_object | 1 |
| author | Sznitman, Alain-Sol 1955- |
| author_GND | (DE-588)1026745527 |
| author_facet | Sznitman, Alain-Sol 1955- |
| author_role | aut |
| author_sort | Sznitman, Alain-Sol 1955- |
| author_variant | a s s ass |
| building | Verbundindex |
| bvnumber | BV011995625 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.75.S95 1998 |
| callnumber-search | QA274.75.S95 1998 |
| callnumber-sort | QA 3274.75 S95 41998 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 SK 920 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)39261919 (DE-599)BVBBV011995625 |
| dewey-full | 530.4/7521 530.4/75 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/75 21 530.4/75 |
| dewey-search | 530.4/75 21 530.4/75 |
| dewey-sort | 3530.4 275 221 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:54Z |
| institution | BVB |
| isbn | 3540645543 9783540645542 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008118400 |
| oclc_num | 39261919 |
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| physical | XVI, 353 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
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| series2 | Springer monographs in mathematics |
| spelling | Sznitman, Alain-Sol 1955- Verfasser (DE-588)1026745527 aut Brownian motion, obstacles and random media Alain-Sol Sznitman Berlin [u.a.] Springer [1998] XVI, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Champs aléatoires Champs aléatoires ram Mouvement brownien, Processus de Mouvement brownien, Processus de ram Waarschijnlijkheidstheorie gtt Wanordelijke media gtt Brownian motion processes Random fields Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Stochastik (DE-588)4121729-9 s DE-604 Zufälliges Feld (DE-588)4191094-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sznitman, Alain-Sol 1955- Brownian motion, obstacles and random media Champs aléatoires Champs aléatoires ram Mouvement brownien, Processus de Mouvement brownien, Processus de ram Waarschijnlijkheidstheorie gtt Wanordelijke media gtt Brownian motion processes Random fields Zufälliges Feld (DE-588)4191094-1 gnd Stochastik (DE-588)4121729-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4121729-9 (DE-588)4128328-4 |
| title | Brownian motion, obstacles and random media |
| title_auth | Brownian motion, obstacles and random media |
| title_exact_search | Brownian motion, obstacles and random media |
| title_full | Brownian motion, obstacles and random media Alain-Sol Sznitman |
| title_fullStr | Brownian motion, obstacles and random media Alain-Sol Sznitman |
| title_full_unstemmed | Brownian motion, obstacles and random media Alain-Sol Sznitman |
| title_short | Brownian motion, obstacles and random media |
| title_sort | brownian motion obstacles and random media |
| topic | Champs aléatoires Champs aléatoires ram Mouvement brownien, Processus de Mouvement brownien, Processus de ram Waarschijnlijkheidstheorie gtt Wanordelijke media gtt Brownian motion processes Random fields Zufälliges Feld (DE-588)4191094-1 gnd Stochastik (DE-588)4121729-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| topic_facet | Champs aléatoires Mouvement brownien, Processus de Waarschijnlijkheidstheorie Wanordelijke media Brownian motion processes Random fields Zufälliges Feld Stochastik Brownsche Bewegung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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